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Throughout middle school, high school, and then college, you learn how math is more than just about numbers. You learn how math is more than just about how many watermelons Sally has remaining after giving 32 watermelons to John. You start to learn about how the Fibonacci sequence shows up in sunflowers, and how polynomials represent data in real life. As a mathematics major, I have taken courses where mathematics becomes, in fact, less about concrete numbers and ventures into the universe of abstraction - where the real beauty of mathematics lives.
During my sophomore year of college, I had the fortunate opportunity to work with my Calculus instructor, Matt*, who was a graduate student at the time. We worked on a reading based off of a topic of interest in mathematics not usually taught in university courses. The topic we ended up focusing on was based off of Matt’s dissertation: tropical mathematics.
Before I could dive into the topic, I of course had to learn how to “read” mathematics. We were reading texts not typically used for university courses. This was the beginning of my transformative experience. Matt sent me readings to do so that I could fill in any holes necessary to start the topic. Mathematics is already a difficult subject to understand when taught by a professor, much less reading about mathematics on your own. Thankfully, Matt was there to guide me and give me advice on how to read mathematics. He said, “it's often beneficial to work out examples as you go, even just rewriting the examples in the book in your own handwriting and words can be helpful.” From this point on, I began reading not harder, but smarter. While I still had a myriad of running questions, the material began to synthesize. It was all about perception - mathematics is commonly seen as either “right” or “wrong,” “true” or “false.” While this is true to some degree, mathematical ideas can be interpreted very differently to everyone, especially in extremely novel concepts, like tropical mathematics. When I first read the material, I was blatantly accepting what the author wrote, only taking in one interpretation of the concept. However, with Matt’s new sound advice, I began jotting down questions, possible counterexamples that refuted the author’s statements, and rewriting how I understood the material in my own way.
In life outside mathematics, I began to experience parallels in terms of how I saw the world. With Matt’s tips on how to read mathematics, tips that seemed only applicable to our reading at first, I started to become more critical of what I saw in the media - news articles about politics, new fads in health and diet, and even celebrity gossip had me thinking about other perspectives or biases. I learned to keep in mind that my interpretation for ideas was most likely different from those of other, seemingly dominant sources, like those of published authors. However, my interpretation was not necessarily wrong.
In a meeting with my community service fraternity executive team, a conflict had arisen on whether to increase the service hour requirements for our members. As an executive team, we wanted to increase service hour requirements so that members could step out of their comfort zone and work with different organizations in the community. However, with this new shift in perspective based off of what I learned from Matt, I objected to my executive team. What if fraternity members simply did not have enough time to fulfill the increased requirements? We are all busy college students, and increasing requirements might start feeling like a chore for the members. In the end, the majority of our members were grateful that we did not increase requirements. My awareness of perspective was able to accommodate our members’ needs.
What started as an extracurricular side project has shifted how I see the world around me. Through the mode of mathematics, a seemingly straightforward subject, I have learned to overestimate the power of perspective. Anything in life that may appear to be simple or unambiguous, I now look at with caution, knowing there are likely multiple facets involved. Likewise, anything that seems too overly complicated, I know to reconfigure in terms of my own understanding, because my interpretation is never incorrect. Mathematics is more than just about watermelons, Sally.
*name has been changed to preserve privacy